Question 890082: If angle ABD= x+25
angle CBD= 3x-10
angle ABC= 75,
What is angle ABC? What is angle CBD?
I'm homeschooled and I do self study. I have 2nd hand books from regular schools. So I dont have a manual. And i dont know what the answer is and i cant check. Please do help me thanks!
Answer by Okamiden(22)   (Show Source):
You can put this solution on YOUR website! This MIGHT be a theorem or rule that is simply given to you somewhere in your book, but you can see it for yourself and understand it better! I've attached a picture of what I mean below.
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Simply, I drew out your 4 points on a graph, at random, to help you notice something:
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http://i.imgur.com/HkbTsh5.png
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As you can see, we have this set up. Notice that the angle ABC is simply the angle ABD + angle CBD. It makes sense, because the segment BD is in both these angles, and your book's theorem is probably something like "ABD + DBC = ABC, assuming ABC is the biggest angle".
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If ABC wasn't the biggest angle, the equation wouldn't work, you'd get a weird result in this case. I don't think the book wants you to explore this possibility.
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Now that we know ABD + CBD = ABC, it's simple.
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x+25 + 3x-10 = 75
4x+15=75
x=15
ABD=x+25=40
CBD=3x-10=35
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